ABurkholder Lab 19

Kinematics of Rotational Motion

‍Method 1:

θ = θ0 + ω0t + .5αt2
α = .340 rad/sec^2

‍Method 2:

Vertical Displacement = .69 m
a = αr a = .0075 m/s^2

Radius of Pulley = .0225
α = a/r α = .32

.32/.3397 = 94.2%
The uncertainty of measurement is agreed by the acceleration values.

The Second Experiment

‍Method 1:

Angular acceleration of rotating apparatus = .3397 rad/s^2

Linear Acceleration of falling mass = .0075 m/s^2

Radius of pulley = .0225

Falling mass (m) = .25 kg

Weight of falling mass (Fw) = 2.45 N

Ft = (.25)(.0075) = T - (.25)(9.8)
Ft = 2.4518 N

I = .0225(2.4819)/(.3397)
I = .1649 kg * m^2

‍Method 2:

I(pulleys) = .00058 kg m^2

Thin Rods: length = .34 m, mass = 74.105 kg

I (thin rods) = .002851 kg * m^2 (times four) = .01141 kg*m^2

Moveable mass: mass = .184 kg distance from center = .33m

I (moveable mass) = .02286 (times four) = .091453 kg*m^2

I = .00058 + .01141 + .091453 = .10344 kg*m^2

(.1649 - .10344)/((.1649 + .10344)/2) * 100 = 45.8% Error so there seems to be little difference

‍Experiment #3

‍Gravitational Potential Energy
Mass = .230 kg

Vertical displacement = 1 m
PE = 2.254 J

‍Translational Kinetic Energy:

t (average) = 14.5 sec
v (average) = .06897 m/s
v (final) = .1379 m/s
KE = .02188 J

‍Rotational Kinetic Energy:

Radius of pulley = .0225 m
w (final) = .5996 rad/s
I = .1649 kg*m^2
KE = .02964 J

KE (total) = .002188 + .02964 = .031824
Error = 194.43%
Friction and human error are the main reasons for the error.